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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.08123 |
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| _version_ | 1866929589124595712 |
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| author | Kirkpatrick, T. R. Belitz, D. |
| author_facet | Kirkpatrick, T. R. Belitz, D. |
| contents | Long-time tails, or algebraic decay of time-correlation functions, have long been known to exist both in many-body systems and in models of non-interacting particles in the presence of quenched disorder that are often referred to as Lorentz models. In the latter, they have been studied extensively by a wide variety of methods, the best known example being what is known as weak-localization effects in disordered systems of non-interacting electrons. This paper provides a unifying, and very simple, approach to all of these effects. We show that simple modifications of the diffusion equation due to either a random diffusion coefficient, or a random scattering potential, accounts for both the decay exponents and the prefactors of the leading long-time tails in the velocity autocorrelation functions of both classical and quantum Lorentz models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08123 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Diffusion, Long-Time Tails, and Localization in Classical and Quantum Lorentz Models: A Unifying Hydrodynamic Approach Kirkpatrick, T. R. Belitz, D. Disordered Systems and Neural Networks Long-time tails, or algebraic decay of time-correlation functions, have long been known to exist both in many-body systems and in models of non-interacting particles in the presence of quenched disorder that are often referred to as Lorentz models. In the latter, they have been studied extensively by a wide variety of methods, the best known example being what is known as weak-localization effects in disordered systems of non-interacting electrons. This paper provides a unifying, and very simple, approach to all of these effects. We show that simple modifications of the diffusion equation due to either a random diffusion coefficient, or a random scattering potential, accounts for both the decay exponents and the prefactors of the leading long-time tails in the velocity autocorrelation functions of both classical and quantum Lorentz models. |
| title | Diffusion, Long-Time Tails, and Localization in Classical and Quantum Lorentz Models: A Unifying Hydrodynamic Approach |
| topic | Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2409.08123 |